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During a debate Wednesday night, Cain said Nancy Pelosi blocked any effort when she was speaker of the House to repeal Democrats' health care overhaul, legislation she helped marshal through. Republicans have since captured control of the House during 2010s midterm elections.

After the debate, he told CNBC he "probably should not have made" that comment.

Cain is facing allegations of unwanted sexual advances and his mocking of the first female House speaker comes as he is trying to steady his presidential bid.

Earlier on Twitter, the former pizza company executive repeated the "Princess Nancy" label as the debate continued.